Factoring the sum or difference of two cubes requires the use
of a special factorization pattern that you need to memorize.
That is:

X 3+ Y 3 = (x + y)(X 2 - XY +
Y 2 )

X 3 -Y 3 = (X - Y)(X 2 + XY +
Y 2 )

The word SOFAS is a mnemonic device to help you
memorize this pattern.

Factoring the sum or difference of 2 cubes yields 2 factors.
One is a binomial factor ( 2 terms) and one is a trinomial factor
(3 terms).

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TO FACTOR

1. Write the binomial factor.

2 Work from the binomial factor to find the trinomial factor.
(After you find the binomial factor, you may use SOFAS to help
with the trinomial factor.)

Example:

Factor X 3 +125 First, find the binomial factor.

ASK!

 What term to the third power
equals X 3 ?

first term

 What is the given sign?

sign

 What number to the third power
equals 125?

second term

Therefore, the binomial factor is (X + 5). Keep the binomial
factor and use SOFAS to build the trinomial power.